The Alliant page on the internet doesn't have lead bullets shown with Bullseye in .357 but in the data for .38 Special +P they have 3.9 grains max for a Speer 158 grain LSWC. The Speer LSWCs are soft swaged and not made for high velocities, which is why they don't show .357 data for it. 2.7 grains of Bullseye with a 148 gr. bullet is near the bottom of the load data in the Speer book but it's a great target load. I'm sure that with a harder cast 158 grain SWC the allowable charge for Bullseye is much higher in .357 Mag.
I'd go get my Speer and Lyman books, but I'm having a bout of laziness right now. I'll look it up later and come back and edit.
Ah, we're back. Speer book 14, 158 grain Speer (soft swaged) SWC in .357 can go 4.8 gr. of Bullseye.
In Lyman 49th a 150 grain hard cast SWC with three driving bands can go 7 grain of BE, a 155 grain with 4 small bands can take 7 grains also and a 160 gr hard cast RN with two big bands and a small one takes 6.9 gr. BE.